To draw ellipse or circle shapes and paths.
In photoshop the oval tool is called the ellipse tool. The keyboard shortcut for all the shape tools is U (press the U key). It will highlight the currently selected shape tool in the tool bar on the left of the photoshop window. If the ellipse tool is not allready showing just click the little triangle in the lower right of the shape tool to bring up all the shape tool options, find the ellipse tool and click it. There is also an ellipse (oval) selection tool called the elliptical marquee tool. The keybaord shortcut is M for the marquee tools. To find it use the same method as above.
Choose Ellipse tool from toolbox, hold down Shift key, click and drag.
Photoshop have Horizontal Type Tool and Horizontal Type Mask Tool which you can use to type text in Photoshop.
Photoshop is not bad, it is simply a tool.
The custom shapes tool can be found in the Photoshop toolbox. You will find it on the same tool icon as the rectangle tool along with ellipse, polygon, line. The 'custom' shapes tool is at the bottom of the list and you then need to select a shape from the shapes palette. Once selected, the shape can be applied as a shape layer, path or fill pixels. Set the color via the foreground color option.
In Photoshop, the pucker tool is part of the Liquify tool. The pucker tool is used to move pixels towards the center of the brush area.
Photoshop is one such tool for that. Pixlr is another tool which can be used like Photoshop.
All tools like Move tool, Brush tool, Type tool live in Toolbox or tool panel as you say. It is one of most important panels in Photoshop, you can not access tools in Photoshop from any other panel in Photoshop.
Photoshop Lightroom does not have such a tool. Anyway you can use external editing software like Photoshop or Photoshop Elements. See related links for more details.
There is no eyelash tool in Photoshop, but you can create a preset paintbrush so you'll only have to design them once.
The Move Tool allows you to rearrange layers in Photoshop by dragging and dropping.
Its the Zoom tool